Use the Mean Value Theorem to prove the inequality |sin(a) - sin(b)| <= |a - b| for all a and b.
The MVT says that there is some c between a and b so sin(a) - sin(b) = cos(c)(a - b). Where do I go from there?
If the two sides are equal, then their absolute values are certainly equal:Use the Mean Value Theorem to prove the inequality |sin(a) - sin(b)| <= |a - b| for all a and b.
The MVT says that there is some c between a and b so sin(a) - sin(b) = cos(c)(a - b).